According to the U.S. Department of Defense, "...the naming convention goes back to before the Air Force split from the Army in 1947 when Army Gen. Hamilton Howze was assigned to Army aviation. His mission was to develop doctrine and the way forward when it came to employing Army aircraft and how they would support warfighters on the ground."
The D.O.D continues, "Howze said since the choppers were fast and agile, they would attack enemy flanks and fade away, similar to the way the tribes on the Great Plains fought during the aforementioned American Indian Wars. He decided the next helicopter produced -- the well-known H-13 of “M.A.S.H.” fame -- would be called the Sioux in honor of the Native Americans who fought Army soldiers in the Sioux Wars and defeated the 7th Calvary Regiment at the Battle of Little Bighorn."
According to AR 70-28, "Army aircraft were specifically categorized as requiring 'Indian terms and names of American Indian tribes and chiefs.' Names to choose from were provided by the Bureau of Indian Affairs."
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Source: U.S. Department of Defense, "Why Army Helicopters Have Native American Names"